Question: What is the greatest common factor of $35b^{2}$, $15b^{3}$, and $5b$ ?
Solution: Let's factor each monomial to its prime factors: $\begin{aligned} 35b^{2}&=(5)(7)(b)(b) \\\\ 15b^{3}&=(3)(5)(b)(b)(b) \\\\ 5b&=(5)(b) \end{aligned}$ We want the largest set of factors that's included in all three monomials. All of the monomials have one factor of $ 5$ and one factor of $ b$ : $\begin{aligned} 35b^{2}&=( 5)(7)( b)(b) \\\\ 15b^{3}&=(3)( 5)( b)(b)(b) \\\\ 5b&=( 5)( b) \end{aligned}$ This is the greatest common factor: $( 5)( b)=5b$